Features
- Fast. Calibrates volatility surfaces in a fraction of a second
- Arbitrage-free. No butterfly or calendar spread arbitrage, including in the tails
- Stable. Variance-space formulation preserves structural consistency of the volatility surface across strikes and maturities
- Intuitive, shape-based parametrization. Direct control over ATM volatility, skew, and overall surface shape
- Universal settings. Same parameters across underlyings and market regimes — no retuning needed
- Rigorous tails. Linear variance in log-strike extrapolation, Lee's tail slope bounds, and closed-form no-arbitrage conditions in the wings
Research
The CVI algorithm is presented in “Convex Volatility Interpolation”, published in Risk magazine, Cutting Edge, February 2026.
The Volptima library goes beyond the paper, incorporating enhanced wing stability for demanding applications such as systematic trading and market making.
Technology
CVI is implemented in Rust and delivered as a library with bindings for Python, C/C++, and other languages. The fitting engine uses the Clarabel interior-point solver to solve a sparse quadratic program jointly encoding market quotes and no-arbitrage conditions. From market data to calibrated surface in a fraction of a second. Available as a cloud API or an on-premise binary for integration into existing trading infrastructure.
Built for options market makers, systematic funds, and trading desks.